Put a rimmed baking sheet in the upper third of the oven and preheat to 475 degrees F. Combine the potatoes, 2 tablespoons olive oil and 1/2 teaspoon herbes de Provence in a large bowl; season generously with salt and pepper. In a separate bowl, combine the beans, 1 tablespoon olive oil and the remaining 1/2 teaspoon herbes de Provence; season generously with salt and pepper.
Remove the hot baking sheet from the oven; add the potatoes in a single layer on one side of the pan and the beans on the other side. Roast until the potatoes are browned and the beans are tender, about 20 minutes.
Meanwhile, combine the tomatoes, olives, remaining 2 tablespoons olive oil, the lemon juice, 1/2 teaspoon salt and a pinch of pepper in a small bowl; set aside. Season the cod all over with salt.
Remove the baking sheet from the oven. Separately stir the potatoes and beans with a spatula and push to the sides of the pan, leaving a space in the middle. Place the cod in the middle of the pan and top with half of the tomato mixture. Roast until the cod is opaque, 10 to 12 minutes. Sprinkle the potatoes with parsley. Serve with the remaining tomato mixture.